The main idea behind the WENO scheme is that it uses a convex combination
of all the ENO candidate sub-stencils in a non-linear manner and assigns
a weight to each sub-stencil between 0 and 1 based on its local
smoothness indicator. The basic strategy of assigning the weights
is that, by the combining of the lower order polynomials with optimal
weights, which yields an upwind scheme of maximum possible order in
smooth regions of the solution and assigns smaller weights to those
lower order polynomials whose stencils contain discontinuities so
that the essentially non-oscillatory property is achieved. The detailed
description of the methodology about ENO and WENO schemes and their
implementation can be found in [1]}, [2]}.
